Patient must be enrolled on the ComboMATCH registration protocol (EAY191) at the time of registration to the EAY191-E4 study

Patient must be >= 18 years of age

Patient must not have any of the following mutations (as determined by the ComboMATCH registration protocol), which are known to confer sensitivity or resistance to nilotinib monotherapy:
* KIT: W557R, V559D, V559A, L576P, and K642E
* PDGFR-alpha: D842V

Patient must have disease that can be safely biopsied and agree to a pre-treatment biopsy or have archival tissue available from within 12 months prior to the date of registration on the ComboMATCH registration trial (EAY191)
* NOTE: The current actionable mutation of interest (aMOI)/actionable alteration list for this treatment trial can be found on the Cancer Trials Support Unit (CTSU) website
* NOTE: Novel/dynamic aMOI can be submitted for review per the process described in the ComboMATCH registration protocol

Patient must be willing to provide blood samples for research purposes

Patient must have had at least one prior line of therapy in the metastatic setting

Patient must have previously undergone taxane therapy (in the metastatic setting)
* Patients who previously responded to prior taxane therapy must have received their last dose of taxane therapy within 6 months prior to EAY191-E4 registration and have had no other intervening treatment prior to EAY191-E4 registration
* Patients who did not respond to prior taxane therapy are eligible regardless of the time elapsed since the prior taxane therapy or any other intervening therapies

Patient must have an Eastern Cooperative Oncology Group (ECOG) performance status of 0-2

Patient must not have had platinum-resistant epithelial serous ovarian cancer

Patient must not have peripheral neuropathy > grade 1

Patients must not have neuropathy >= grade 2 within 14 days of registration/randomization

Patient must have documented QT interval with Fridericia’s correction (QTcF) of =< 450 msec within 8 days prior to EAY191-E4 registration. Patients with a QTcF interval of >= 450 msec at registration or patients with congenital long QT syndrome are not eligible

Patient must not be pregnant or breast-feeding due to the potential harm to an unborn fetus and possible risk for adverse events in nursing infants with the treatment regimens being used
* All patients of childbearing potential must have a blood test or urine study within 14 days prior to registration to rule out pregnancy
* A patient of childbearing potential is defined as anyone, regardless of sexual orientation or whether they have undergone tubal ligation, who meets the following criteria: 1) has achieved menarche at some point, 2) has not undergone a hysterectomy or bilateral oophorectomy; or 3) has not been naturally postmenopausal (amenorrhea following cancer therapy does not rule out childbearing potential) for at least 24 consecutive months (i.e., has had menses at any time in the preceding 24 consecutive months)

Patient must not expect to conceive or father children by using accepted and effective method(s) of contraception or by abstaining from sexual intercourse for the duration of their participation in the study and for at least 3 months after the last dose of study drug

Patients must have progressive disease

Absolute neutrophil count (ANC) >= 1,500/mcL

Platelets >= 100,000/mcL

Total bilirubin =< 1.5 x institutional upper limit of normal (ULN) (with the exception of those with Gilbert syndrome, who must have total bilirubin =< 3 x institutional ULN)

Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase [SGOT])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase [SGPT]) =< 3 institutional upper limit of normal; < 5.0 x ULN in patients with liver metastases

Creatinine clearance > 60 mL/min/1.73 m^2 for patients with creatinine levels > 1.5 mg/dL

Patient must have the ability to swallow medications

PRIMARY OBJECTIVE:
I. To evaluate the proportion of patients with taxane-refractory advanced malignancies who have objective responses (OR) to treatment with nilotinib hydrochloride monohydrate (nilotinib) and paclitaxel.

SECONDARY OBJECTIVE:
I. Collect tissue and provide it to the ComboMATCH registration protocol to assess concordance between the diagnostic tumor mutation profile generated by the designated laboratories, the pre-treatment biopsy mutation profile, and the pre-treatment circulating tumor deoxyribonucleic acid (ctDNA) mutation profile from plasma, as described in ComboMATCH registration protocol. For this treatment substudy, the outcome objective will be to report the proportion of cases providing sufficient tissue for that integrated scientific activity in the ComboMATCH registration protocol.

EXPLORATORY OBJECTIVES:
I. To evaluate progression free survival (PFS) at 6 months on study agents.
II. To identify genomic and transcriptomic determinants of response and resistance in tumor biopsy specimens and cell-free deoxyribonucleic acid (DNA).

OUTLINE:
Patients receive nilotinib hydrochloride monohydrate orally (PO) twice daily (BID) on days 1-28 and paclitaxel intravenously (IV) over 1 hour on days 1, 8, and 15 of each cycle. Cycles repeat every 28 days in the absence of disease progression or unacceptable toxicity. Patients undergo computed tomography (CT) or magnetic resonance imaging (MRI) throughout the study. Patients also undergo collection of blood samples and tumor biopsy on study.

After completion of study treatment, patients are followed until disease progression, and for survival for 3 years from registration.